Related papers: New density/likelihood representations for Gibbs m…
Point processes are a useful mathematical tool for describing events over time, and so there are many recent approaches for representing and learning them. One notable open question is how to precisely describe the flexibility of point…
We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate…
In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the…
This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for…
By making use of the familiar Mathieu series and its generalizations, the authors derive a number of new integral representations and present a systematic study of probability density functions and probability distributions associated with…
The new class of Markov processes is proposed to realize the flexible shrinkage effects for the dynamic models. The transition density of the new process consists of two penalty functions, similarly to Bayesian fused LASSO in its functional…
We construct Gibbs perturbations of the Gamma process on $\mathbbm{R}^d$, which may be used in applications to model systems of densely distributed particles. First we propose a definition of Gibbs measures over the cone of discrete Radon…
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…
Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…
We present a simple derivation of the stochastic equation obeyed by the density function for a system of Langevin processes interacting via a pairwise potential. The resulting equation is considerably different from the phenomenological…
We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the…
Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…
We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the…
This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…
Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events of particle occurrences at (histogram-resolved) space points. Here we investigate an alternative method based on a…
We consider a generalization of the classifier-based density-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. The problem with most loss functions used for this task is that they implicitly…
Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…
This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…
We report on probability-density-functions (PDF) of the mass density in numerical simulations of highly compressible hydrodynamic flows and the corresponding structure formation of Lagrangian particles advected by the flows. Numerical…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…